3 Answers
3

Sh'miras Shabas K'hilchasah 20:19–20 says they are muktzim mechamas chisaron kis (muktze because of potential loss of value), which is one of the 'severe' types of muktze, so they can't be moved even if one needs them or their spot. He doesn't differentiate among blank checks, signed checks, and cleared checks. As always, for practical halacha, CYLOR.

Items which have no purpose on Shabbos (or no designated purpose at all, and kept that status when shabbos arrived) are categorized as muktza machamas gufo (intrinsically muktza).

(Tom wanted to call it machmas issur because it had a designated pupose, but was unusable because using a check is forbidden on shabbos. I have seen muktza machmas issur normally applied to an item which is intrinsically purposeful on Shabbos, but the is an extrinsic issur in it's usage, like the case of a garment of shaatnez).

Why does a check have no purpose? It can be used to pay, which would seem to make it merely k'li shem'lachto l'isur, not muktze mechamas gufo.
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msh210♦Aug 4 '11 at 4:28

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Kli shemelachto l'issur is where there is an item which is usable on shabbos, but its primary purpose is for issur. Since it is usable, he does not mentally eliminate its use for shabbos (that's why he can move it for the useful purpose- l'gufo or mekomo). An item which has no permissible use on shabbos is fully muktza- he has mentally eliminated its use for shabbos.
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YDKAug 4 '11 at 20:44

A question you can ask is: Is a check (or any shtar) a kli? If it is, then it had to be considered under the category of "kol hakelim nitalim chutz mimuktza machmas chisaron kis" so it can only be considered fully muktza if you hold like your SS"K. But I don't think it is a kli, since its use is what it represents, not what it does.
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YDKAug 4 '11 at 20:47